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The Conjugacy Ratio of Groups

Part of: Probabilistic methods in group theory Special aspects of infinite or finite groups

Published online by Cambridge University Press:  22 February 2019

Laura Ciobanu ,
Charles Garnet Cox  and
Armando Martino
Laura Ciobanu
Affiliation:
Heriot-Watt University, Edinburgh, EH14 4AS, UK (l.ciobanu@hw.ac.uk)
Charles Garnet Cox
Affiliation:
University of Bath, BA2 7AY, UK (cpgc20@bath.ac.uk)
Armando Martino
Affiliation:
Mathematical Sciences, University of Southampton, SO17 1BJ, UK (A.Martino@soton.ac.uk)
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Abstract

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In this paper we introduce and study the conjugacy ratio of a finitely generated group, which is the limit at infinity of the quotient of the conjugacy and standard growth functions. We conjecture that the conjugacy ratio is 0 for all groups except the virtually abelian ones, and confirm this conjecture for certain residually finite groups of subexponential growth, hyperbolic groups, right-angled Artin groups and the lamplighter group.

Keywords

conjugacy growthdegree of commutativitypolynomial growthRAAGshyperbolic groupswreath products

MSC classification

Primary: 20P05: Probabilistic methods in group theory
Secondary: 20F69: Asymptotic properties of groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 3 , August 2019 , pp. 895 - 911
Copyright
Copyright © Edinburgh Mathematical Society 2019 

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